Mixed Finite Element Methods and Applications
By: by Daniele Boffi, Franco Brezzi, Michel Fortin
Contributors: Brezzi, Franco; Fortin, Michel; SpringerLink (Online service)
Series: Springer Series in Computational Mathematics -- 44
Published: 2013
Language: eng
Format: [electronic resource] /
Number of pages: 685
ISBN-13: 9783642365195
Subjects: Computational Mathematics and Numerical Analysis; Theoretical and Applied Mechanics; Applied Mechanics; Mathematics; Computational Science and Engineering; Computer science
Description: Non-standard finite element methods, in particular mixed methods, are central to many applications. In this text the authors, Boffi, Brezzi and Fortin present a general framework, starting with a finite dimensional presentation, then moving on to formulation in Hilbert spaces and finally considering approximations, including stabilized methods and eigenvalue problems. This book also provides an introduction to standard finite element approximations, followed by the construction of elements for the approximation of mixed formulations in H(div) and H(curl). The general theory is applied to some classical examples: Dirichlet's problem, Stokes' problem,  plate problems, elasticity and electromagnetism.
Table of contents: title: Preface; title: Variational Formulations and Finite Element Methods; title: Function Spaces and Finite Element Approximations; title: Algebraic Aspects of Saddle Point Problems; title: Saddle Point Problems in Hilbert spaces; title: Approximation of Saddle Point Problems; title: Complements: Stabilisation Methods, Eigenvalue Problems; title: Mixed Methods for Elliptic Problems; title: Incompressible Materials and Flow Problems; title: Complements on Elasticity Problems; title: Complements on Plate Problems; title: Mixed Finite Elements for Electromagnetic Problems; title: Index.        .